Windmill Pivot

Consider a set of points P in the plane such that no 3 points are collinear. Construct a windmill as follows:

• Choose a point p ∈ P and a starting direction such that the line through p in that direction does not intersect any other points in P. Draw that line (Note: line, NOT ray).
• Rotate the line clockwise like a windmill about the point p as its pivot until the line intersects another point q ∈ P. Designate that point q to be the new pivot, and then continue the rotation. This is called promoting point q.
• Continue this process until the line has rotated a full 360°, returning to its original direction (it can be shown that the line will also return to its original position after a 360° rotation).

During this process, a given point in P can be a pivot multiple times. Considering all possible starting pivots and orientations, find the maximum number of times that a single point can be promoted during a single 360° rotation of a windmill. Note that the first point is a pivot, but not promoted to be a pivot at the start.

The first line of input contains a single integer n (2 ≤ n ≤ 2000), which is the number of points p ∈ P.

Each of the next n lines contains two space-separated integers x and y (−105 ≤ x, y ≤ 105). These are the points. Each point will be unique, and no three points will be collinear.

Output a single integer, which is the maximum number of times any point p ∈ P can be promoted, considering a full 360° rotation and any arbitrary starting point.